Blender 2.8 exports fbx with flipped normals
Check Face Orientation in the Overlays popover:



In my opinion, in the 2.80 it's harder to recognize a inverted normals in default shading.

Also check, that your object doesn't have negative scale. 

Edit: The negative scale can be a byproduct of mirroring (Crtl M) while in object mode. To combat this, mirror the object while in edit mode, and then flip the normals of the mirrored part. Recalculating Normals works just as well.